This note presents the measurement of inclusive-jet cross-sections in proton--proton collisions at a centre-of-mass energy of 13TeV. The measurement uses data corresponding to an integrated luminosity of 3.2 fb$^{-1}$ collected with the ATLAS detector at the Large Hadron Collider in 2015. Jets are clustered using the anti-$k_\text{t}$ algorithm with a radius parameter value of $R = 0.4$. Double differential inclusive-jet cross-sections are presented as a function of the jet transverse momentum, covering the range from 100 GeV to about 3.2 TeV, and of the absolute jet rapidity, up to $|y| = 3$. The predictions of next-to-leading-order QCD calculations using several parton distribution function (PDF) sets and corrected for non-perturbative and electroweak effects are compared to the measured cross-sections. The predictions are consistent with the measured cross-sections within uncertainties.